5 Arbitrage and Interest Rates
Recall that most foreign currency operations involve bank deposits. A bank deposit is an
asset that generates interest for the depositor. The decision of where to maintain deposits
is largely a matter of convenience for most. However, for investors, this decision is
known as uncovered interest parity (UIP).
To hedge against exchange rate risk, investors can use derivatives such as forwards.
In this way, the arbitrager eliminates exchange rate risk, that is, he or she is “covered.”
Riskless Arbitrage: Covered Interest Parity
This presentation mirrors the one in the text, but makes use of different exchange rates.
Riskless arbitrage refers to arbitrage that does not involve exchange rate risk. To
Suppose that an American investor Katya is considering whether to put her $800
savings into a U.S. bank account or in a British bank account for the next year. She must
evaluate the expected rate of return from these two investment strategies. (The numbers
used in this example approximate the actual values of the variables as of October 12,
The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This
is the gross dollar return Katya receives from her investment at the end of one year. For
This gain or loss is determined by the forward exchange rate, F$/£ (1.6090), and the
current spot rate, E$/£ (1.6114). Converting one U.S. dollar into British pounds would cost
the forward rate would yield F$/£ dollars. Therefore, the return on British deposits, in U.S.
dollars, is
Utilizing the figures given above, we can use any three variables to calculate the
implied value of the remaining one. For example, the implied value of F$/£ is 1.6076. The
condition yields
APPLICATION
Evidence on Covered Interest Parity
To test whether covered interest parity holds, we can determine whether foreign
exchange traders could, in fact, earn a profit through establishing forward and spot
The data illustrate that arbitrage led to zero profits in the absence of capital controls.
When capital controls are removed, arbitrage profits decrease.
As financial systems become more liberalized, arbitrage opportunities disappear
quickly. When governments imposed capital controls in the foreign exchange market,
Risky Arbitrage: Uncovered Interest Parity
Risky arbitrage does not “cover” investors with a forward contract. Instead, investors
must make their decisions based on what they think the exchange rate will be in the
future. The expected future exchange rate replaces the forward exchange rate in the CIP
example shown previously, and repeated below.
The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This
is the gross dollar return Katya receives from her investment at the end of one year. For
We call this the expected exchange rate, Ee$/£. Given the current spot rate, E$/£ (1.6114)
and the interest rates on the two accounts, we can calculate the market’s forecast of the
But, unlike covered interest parity, the forward exchange rate is not known. The
unknown variable in the uncovered interest parity equation is the expected exchange rate
APPLICATION
Evidence on Uncovered Interest Parity
If the UIP and CIP hold, this implies the forward exchange rate is equal to the expected
future exchange rate. If we divide the CIP condition by the UIP condition, we get
Canceling terms yields
The expression on the left-hand side is the forward premium. To estimate the right-
Uncovered Interest Parity: A Useful Approximation
It will be convenient to use the following approximation:
UIP provides a theory of how expectations are linked to the current spot exchange
rate and to interest rates across countries. Rewriting the UIP condition yields
know that investors expect that the U.S. dollar will depreciate:
6 Conclusions
This chapter provides an overview of exchange rates, the forex market, and the
conditions defining equilibrium in the market, and discusses the ways in which private
actors and the government participate in the forex market. Although there are mainly two
S I D E B A R
Assets and Their Attributes
Investors have many options in holding their wealth. There are many available assets:
cash, stocks, bonds, bank deposits, real estate, and so on. Investors make choices about
how to hold their wealth based on three criteria:
• Rate of return: the net increase in wealth generated from holding the asset.
and services (e.g., the ease with which it can be liquidated or sold). Investors
prefer more liquid assets.
These observations lead to two conclusions. First, investors are willing to trade off more
Teaching Tips
Teaching Tip 1: Uncovered interest parity says the difference between the U.S. interest
rate and the foreign interest rate should equal the expected rate of depreciation of the U.S.
dollar. The Excel workbook for this chapter includes a worksheet that shows comparable
2009 interest rates for a number of countries as well as for the United States. The United
States – foreign difference is also included. Show this table to your students and ask them
to discuss the results. For example, Iceland’s currency is expected to appreciate by
Teaching Tip 2: In this chapter, we assumed frictionless trading in the forex market.
This assumption is relaxed in the last chapter of the textbook. For now, explore the bid-
ask spread with your students. The bid price is the price at which a dealer is willing to
sell a security or currency. The ask price is the willingness-to–buy price. Dealers make a
living on the bid-ask spread. In foreign currency markets, this spread is quoted in pips.
For most currencies, a pip is equal to 0.0001 on the exchange rate. For the yen, however,
one pip is 0.01 of the exchange rate. Exchange rates are conventionally quoted as foreign
currency per U.S. dollar. For example, in the euro–U. S. dollar market, suppose the bid
price is 1.4745 and the ask price is 1.4746. The spread is 1 pip. OANDA’s website offers
a complete list of bid–ask spreads for its trades
IN–CLASS PROBLEMS
1. Use Table 13-1 in the textbook to answer the following questions:
Exchange Rates on June 30, 2009
(one year previous)